Solve (1- x2)y" +2xy'-2y = 0 on (-1,1) given that y1 = x is a solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Solve the differential equation e2d = e-y- 2xe3-y.
2. Solve the differential equation x- 2y = x cos() on (0, o).
3. Show that the differential equation
(1– 2y + x In r)dr + (ev – 2x)dy = 0
is exact and find its solutions.
4. Solve (1- ²)y" + 2xy' - 2y = 0 on (-1, 1) given that y1 = x is a solution.
5. (a) Solve the initial-value problem 2y" + y'-y = 0, y(0) = 0, y'(0) = 1.
(b) Solve the differential equation y"+ 4y'+8y = 0.
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